Florianópolis is not really a city you visit, it's an island you move around. Most of the municipality is Ilha de Santa Catarina, a 54 km strip of land with more than 100 beaches, a big lagoon in the middle and hills in between. The old town sits on the west coast, facing the mainland, and it was founded in the 17th century as Nossa Senhora do Desterro. Azorean and Madeiran settlers arrived by the thousands in the 1740s and 1750s, and their fishing villages, churches and oyster farms are still part of the island's character. The Hercílio Luz Bridge, opened in 1926, is the postcard, but the real reason people come is the coast.
The coast comes in two moods. The north bay side is sheltered and calm, which is why Jurerê and the family beaches are there. The Atlantic side to the east and south is open sea: surf, wind, dunes and cold water. You'll want both, and you'll want to know which one you're standing on. Five days is a good length for this. It gives you one day per island part (north, east, south-east, far south with Campeche island) and a day for the city, with enough slack to lose a day to rain or wind, which happens.
This plan runs in that order: day one is the north, day two the east beaches around the lagoon, day three the south-east with the Lagoinha do Leste trail and the oyster coast, day four the Campeche island boat trip and the far south, and day five the old centre. It assumes a rental car for at least four of the days, and the practical sections explain why. Start on a Tuesday: the fortresses are closed on Mondays, Projeto Tamar is closed on Tuesdays (day two is a Wednesday), and day five lands on a Saturday, when the central market is fully open. It's also a good first look at Brazil for a beach trip, with the food, the snack bars and the weekend habits you'll meet in the rest of the country.